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A214011
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T(n,k) is the number of n X n nonnegative integer matrices with row and column i=1..n having sum <= i*k.
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10
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2, 3, 12, 4, 54, 271, 5, 160, 7722, 24950, 6, 375, 85639, 9318805, 9800058, 7, 756, 564041, 641631566, 98721672541, 16942485560, 8, 1372, 2663506, 17609835599, 69768979161580, 9463992096711104, 131898088386405, 9, 2304, 9976732
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OFFSET
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1,1
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COMMENTS
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Table starts
2, 3, 4, 5, 6;
12, 54, 160, 375, 756;
271, 7722, 85639, 564041, 2663506;
24950, 9318805, 641631566, 17609835599, 269462676001;
9800058, 98721672541, 69768979161580, 11798463876314995, 807203255071567008.
T(n,k) is the number of integer lattice points in kP where P is an (n^2)-dimensional polytope with vertices having integer coordinates. Therefore row n is an Ehrhart polynomial in k, with degree n^2 and rational coefficients. (End)
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LINKS
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FORMULA
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Empirical: rows 1 2 3 are polynomials of degree 1 4 9.
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EXAMPLE
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Some solutions for n=3, k=1:
0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0
1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 2
0 0 1 0 0 1 1 2 0 0 0 0 0 1 1 0 0 2 0 0 0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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